A note on the necessity of filtering mechanism for polynomial observability of time-discrete wave equation

The problem of uniform polynomial observability was recently analyzed. It is shown that, when the continuous model is uniformly polynomially observable, it is sufficient to filter initial data to derive uniform polynomial observability inequalities for suitable time-discretization schemes. In this note, we prove that a filtering mechanism of high frequency modes is necessary to obtain uniform polynomial observability. More precisely, we give a counterexample which proves that this latter fails without filtering the initial data for time semi-discrete approximations of the wave equation

Uniform boundary controllability of a discrete 1-D Schrodinger equation

In this paper we study the controllability of a finite dimensional system obtained by discretizing in space and time the linear 1-D Schrodinger equation with a boundary control. As for other problems, we can expect that the uniform controllability does not hold in general due to high frequency spurious modes. Based on a uniform boundary observability estimate for filtered solutions of the corresponding conservative discrete system, we show the uniform controllability of the projection of the solutions over the space generated by the remaining eigenmodes

Aspects épidémiologiques et cliniques de la leishmaniose cutanée à Kairouan-Tunisie et particularités chez l'enfant.

International audienceCutaneous leishmaniasis (CL) remains highly endemic in Tunisia. The governorate of Kairouan (Center) is one of the most affected particularly by zoonotic form due to Leishmania major. The purpose of this study was to describe the epidemiological, clinical and therapeutic features of the disease in this governorate and to identify any particularities in children. Three hundred and ninety cases were registered over 2 years (2012 and 2013). The average age was 29 years one month [± 22.7] (34.6% of patients were under 15 years). The cumulative incidence of CL was equal to 34.4 per 100,000 per year. It was higher in children (39.6 per 100,000 versus 29, p=0.004). Cases were diagnosed especially in autumn and winter (88.3% of cases between October and January, p<0.001). The average delay of consultation was one month and 22 days [± 2.5] after onset of lesions. The average number of lesions per patient was 2.7 [± 2.3] with a mean diameter equal to 2.2 cm. In addition to a higher incidence of the disease, two other features were found in "Children" group which are the presence of similar cases in the neighborhood (27.7% versus 13.4%, p=0.002) and preferential localization in the face (36.4% versus 11%) while the members were more affected in adults (63.5% versus 46.4%) (p<0.001). Meglumine antimoniate was prescribed for most of our patients (93.1%). The intramuscular route was used more than local one, probably because of high proportions of multiple lesions and facial localization.La leishmaniose cutanée (LC) reste fortement endémique en Tunisie. Le gouvernorat de Kairouan (Centre) est l’un des plus concerné particulièrement par la forme zoonotique à Leishmania major. L’objectif de cette étude était de décrire les aspects épidémiologiques, cliniques et thérapeutiques de la maladie dans le gouvernorat de Kairouan et d’identifier les particularités clinico-épidémiologiques chez l’enfant. Trois-cent-quatre-vingt-dix cas ont été colligés sur 2 ans (2012 et 2013) à partir des cas déclarés aux autorités sanitaires régionales. La moyenne d’âge était de 29 ans et un mois [± 22,7] (34,6 % des patients avaient moins de 15 ans). L’incidence cumulée globale de la LC était égale à 34,4/100 000 habitants et par an; plus élevée chez les enfants (39,6 versus 29 pour 100 000, p=0,004). Les cas étaient diagnostiqués surtout à la période automno-hivernale (88,3 % des cas entre octobre et janvier, p<0,001). Le délai moyen de consultation était de un mois et 22 jours [± 2,5] après l’apparition des lésions. Le nombre moyen de lésions par patient était de 2,7 [± 2,3] avec un diamètre égal à 2,2 cm en moyenne. En plus d’une plus forte incidence de la maladie, deux autres particularités ont été relevées dans le groupe « Enfants », à savoir la présence de cas similaires dans l’entourage (27,7 % versus 13,4 %, p=0,002) et une localisation préférentielle au visage (36,4 % versus 11 %) alors que les membres étaient davantage touchés chez l’adulte (63,5 % versus 46,4 %) (p<0,001). L’antimoniate de méglumine (AM) a été prescrit à presque tous nos malades (93,1 %). La voie intra musculaire a été plus utilisée que celle locale en raison probablement des proportions importantes de lésions multiples et de l’atteinte faciale

Procalcitonin biomarker kinetics fails to predict treatment response in perioperative abdominal infection with septic shock

Introduction: Procalcitonin (PCT) biomarker is suggested to tailor antibiotic therapy in the medical intensive care unit (ICU) but studies in perioperative medicine are scarce. The aim of this study was to determine whether PCT reported thresholds are associated with the initial treatment response in perioperative septic shock secondary to intra-abdominal infection. Methods: This single ICU, observational study included patients with perioperative septic shocks secondary to intra-abdominal infection. Demographics, PCT at days 0, 1, 3, 5, treatment response and outcome were collected. Treatment failure included death related to the initial infection, second source control treatment or a new onset intra-abdominal infection. The primary endpoint was to assess whether PCT thresholds (0.5 ng/ml or a drop from the peak of at least 80%) predict the initial treatment response. Results: We included 101 consecutive cases. Initial treatment failed in 36 patients with a subsequent mortality of 75%. Upon admission, PCT was doubled when treatment ultimately failed (21.7 ng/ml +/- 38.7 vs. 41.7 ng/ml +/- 75.7; P = 0.04). Although 95% of the patients in whom PCT dropped down below 0.5 ng/ml responded to treatment, 50% of the patients in whom PCT remained above 0.5 ng/ml also responded successfully to treatment. Moreover, despite a PCT drop of at least 80%, 40% of patients had treatment failure. Conclusions: In perioperative intra-abdominal infections with shock, PCT decrease to 0.5 ng/ml lacked sensitivity to predict treatment response and its decrease of at least 80% from its peak failed to accurately predict treatment response. Studies in perioperative severe infections are needed before using PCT to tailor antibiotic use in this population